JDM's are a rubbish programmer to start with, but they certainly won't work with a USB/Serial converter - you need a real serial port, or preferably a better programmer.
The days of parallel/serial port programmers are long gone now, I would strongly suggest you buy a PICKit2 or PICKit3, I've been using a PICKit2 for a couple of years now and it's great, I've also recently (a week ago) bought a PICKit3 in order to support a new PIC that I've started using, the enhanced 14 bit 16F1827 - it's a really nice chip, with lot's of nice features, and it's cheaper than the older 16F series.
The PICKit3 doesn't currently have the serial and logic analysers that the PICKit2 does, which is a shame - but neither did the PICKit2 originally, it was added in a later software update - apart from that, and the bright red colour
I'm just as pleased with the 3.